"Give examples of values of n and p,..." was answered by students like you

CheemnCatelvew

Answered question

2021-09-21

Give examples of values of n and p, both non-zero, for a binomial random variable X. Use either the binomial probability formula or the binomial probability cumulative distribution tables provided in class to calculate:
a) $P (X = x_{0})$ where $x_{0}$ is an integer of your own choice satisfying

$0 < x_{0} < n$ .
b) $P (X > x_{0})$

Answer & Explanation

liingliing8

Skilled2021-09-22Added 95 answers

Step 1
Let $n = 5$ and $p = 0.5$
Let X be the binomial random variable following a binomial distribution Bin $(n = 5, p = 0.5)$
Therefore, according to binomial probability distribution
$(X = x) =^{n} C_{x} \times p^{x} \times {(1 - p)}^{x}$
Step 2
Let $x_{0}$ be 2
a).Therefore, according to binomial probability formula-
$(X = 2) =^{5} C_{2} \times {(0.5)}^{2} \times {(1 - 0.5)}^{5 - 2}$
$= \frac{5!}{2! \times 3!} \times {(0.5)}^{2} \times {(0.5)}^{3}$
$= 0.3125$
b).
$P (X > 2) = 1 - P (X \leq 2)$
$= 1 - [P (X = 0) + P (X = 1) + P (X = 2)]$
$= 1$
$\leq f t \leq f t {[^{{5}} C_{0} \times {(0.5)}^{0} \times {(1 - 0.5)}^{5 - 0}] + [^{{5}} C_{1} \times {(0.5)}^{1} \times {(1 - 0.5)}^{5 - 1}] + [^{{5}} C_{2} \times {(0.5)}^{2} \times {(1 - 0.5)}^{5 - 2}] r i g h t r i g h t r i g h t}$
$= 1 - \leq f t {[1 \times 1 \times {(0.5)}^{5}] + [5 \times {(0.5)}^{1} \times {(0.5)}^{4}] + [\frac{5!}{2! \times 3!} \times {(0.5)}^{2} \times {(0.5)}^{3}] r i g h t}$
$= 1 - 0.5$
$= 0.5$

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